You draw two cards from a standard deck of 52 cards, but before you draw the sec

Question

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck, a) Are the outcomes on the two cards independent? Why? No. The probability of drawing a specific second card depends on the identity of the first card. Yes. The events can occur together. No. The events cannot occur together. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. (b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.) Enter a fraction, integer, or exact decimal. Do not approximate. (c) Find P(king on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)

Explanation / Answer

a)

Since First card drawn does not affect second card drawing, probability of drawing a specific second card is the same

regardless of the identity of the first drawn card.

b)

p(Ace one first card ) = 4/52

p(king on secon card) = 4/52 ( Since first card is put back there is 52 cards for second choice).

p(Ace on first card and king on second card) = 4/52 * 4/52 = 1/169.

c)

P(king on first card and ace on second) = 4/52 * 4/52 = 1/169.

d)

p(Ace and a king in either order) = p(Ace on first card and king on second card)

                                                      + P(king on first card and ace on second)

                                                     = 1/169 + 1/169

                                                     = 2/169

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